You’re reading a lot more into the spec. than I am!
AFAIK sRGB isn’t meant to be aproximately the same primaries as Rec.709, it’s meant to be exactly the same primaries.
Well, no:
Fwd matrix:
0.4124, 0.3576, 0.1805
0.2126, 0.7152, 0.0722
0.0193, 0.1192, 0.9505
Inverse bwd matrix:
3.240625477320053 -1.537207972210319 -0.498628598698248
-0.968930714729319 1.875756060885241 0.041517523842954
0.055710120445511 -0.204021050598487 1.056995942254388
Bwd matrix:
3.2406, -1.5372, -0.4986
-0.9689, 1.8758, 0.0415
0.0557, -0.2040, 1.0570
Inverse bwd matrix:
3.240577163864186 -1.537114442037019 -0.498626528524369
-0.968926691985616 1.875748273242875 0.041517351473191
0.055812535603688 -0.204219316429837 + 1.056991553887184
Saying they match within the precision given, is the same as saying they match as long as you throw away the parts that don’t match!
[ Fixed fwd matrix number - they still don’t match ]